At What Rate Is Heat Being Lost Through The Window By Conduction?

Windows are glazed apertures in the building envelope that typically consist of single or multiple glazing (drinking glass or plastic), framing, and shading. In a building envelope, windows offering the least resistance to heat transfer. In a typical- house, about one-third of the total heat loss in wintertime occurs through the windows. Likewise, virtually air infiltration occurs at the edges of the windows. The solar heat gain through the windows is responsible for much of the cooling load in summer. The net effect of a window on the heat balance of a building depends on the characteristics and orientation of the window as well as the solar and conditions data. Workmanship is very important in the structure and installation of windows to provide effective sealing around the edges while assuasive them to be opened and closed easily.

Despite being so undesirable from an energy conservation point of view, windows are an essential part of any edifice envelope since they enhance the appearance of the building, allow daylight and solar estrus to come in, and allow people to view and observe outside without leaving their home. For depression-rise buildings, windows also provide easy exit areas during emergencies such as burn. Important considerations in the selection of windows are thermal comfort and energy conservation. A window should have a practiced light transmittance while providing effective resistance to rut transfer. The lighting requirements of a building can exist minimized by maximizing the use of natural daylight. Heat loss in wintertime through the windows can be minimized past using airtight double- or triple-pane windows with spectrally selective films or coatings, and letting in equally much solar radiations as possible. Estrus proceeds and thus cooling load in summertime tin be minimized by using effective internal or external shading on the windows.

Figure 41
The 3 regions of a window considered in estrus transfer assay.

Even in the absence of solar radiations and air infiltration, oestrus transfer through the windows is more complicated than information technology appears to be. This is considering the structure and properties of the frame are quite different than the glazing. Equally a result, heat transfer through the frame and the edge section of the glazing adjacent to the frame is 2-dimensional. Therefore, information technology is customary to consider the window in iii regions when analyzing rut transfer through it: (1) the centre-of-glass, (2) the edge-of-glass, and (3) the frame regions, every bit shown in Fig. 41. Then the total charge per unit of estrus transfer through the window is determined by calculation the heat transfer through each region equally

where

is the U-factor or the overall estrus transfer coefficient of the window; A_window is the window area; A_center, A_edge, and A_frame are the areas of the centre, edge, and frame sections of the window, respectively; and U_centre, U_edge, and U_frame are the heat transfer coefficients for the center, edge, and frame sections of the window. Note that A_window = A_middle + A_edge + A_frame, and the overall U_factor of the window is determined from the area-weighed U-factors of each region of the window. Also, the inverse of the U-factor is the R-value, which is the unit thermal resistance of the window (thermal resistance for a unit area).

FIGURE 42
The thermal resistance network for oestrus transfer through a single glass.

Consider steady one-dimensional heat transfer through a unmarried-pane drinking glass of thickness 50 and thermal electrical conductivity thousand. The thermal resistance network of this trouble consists of surface resistances on the inner and outer surfaces and the conduction resistance of the glass in serial, equally shown in Fig. 42, and the full resistance on a unit area basis can exist expressed as

Using common values of 3 mm for the thickness and 0.92 Westward/k · ºC for the thermal conductivity of the glass and the winter design values of 8.29 and 34.0 W/m² · ºC for the inner and outer surface estrus transfer coefficients, the thermal resistance of the glass is adamant to exist

Notation that the ratio of the glass resistance to the total resistance is

That is, the glass layer itself contributes about 2 per centum of the full thermal resistance of the window, which is negligible. The state of affairs would not be much different if we used acrylic, whose thermal electrical conductivity is 0.nineteen Due west/g · ºC, instead of glass. Therefore, we cannot reduce the heat transfer through the window effectively past simply increasing the thickness of the glass. Only we can reduce it by trapping nevertheless air betwixt ii layers of drinking glass. The result is a double-pane window, which has become the norm in window structure.

FIGURE 43
The thermal resistance network for heat transfer through the center section of a double-pane window (the resistances of the glasses are neglected).

The thermal conductivity of air at room temperature is k_air = 0.025 W/k · ºC, which is one-thirtieth that of glass. Therefore, the thermal resistance of 1-cm-thick nonetheless air is equivalent to the thermal resistance of a 30-cm-thick glass layer. Disregarding the thermal resistances of glass layers, the thermal resistance and U-factor of a double-pane window can exist expressed equally (Fig. 43)

where h_infinite = h_rad, space + h_conv, infinite is the combined radiations and convection heat transfer coefficient of the space trapped between the two glass layers.

Roughly half of the heat transfer through the air infinite of a double-pane window is past radiation and the other half is by conduction (or convection, if there is whatsoever air motion). Therefore, in that location are 2 ways to minimize h_space and thus the rate of heat transfer through a double-pane window:

1. Minimize radiations heat transfer through the air space. This can be
done by reducing the emissivity of drinking glass surfaces by coating them with
low-emissivity (or "depression-eastward" for brusque) material. Call back that the constructive
emissivity of ii parallel plates of emissivities ε_i and ε₂ is given by

The emissivity of an ordinary drinking glass surface is 0.84. Therefore, the effective emissivity of two parallel drinking glass surfaces facing each other is 0.72. Merely when the glass surfaces are coated with a film that has an emissivity of 0.1, the constructive emissivity reduces to 0.05, which is one-fourteenth of 0.72. So for the aforementioned surface temperatures, radiation heat transfer will also become downward by a factor of xiv. Even if only ane of the surfaces is coated, the overall emissivity reduces to 0.i, which is the emissivity of the blanket. Thus it is no surprise that about one-quaternary of all windows sold for residences have a depression-eastward coating. The rut transfer coefficient h_infinite for the air space trapped betwixt the two vertical parallel glass layers is given in Table 16 for thirteen-mm- (1/2-in) and 6-mm- (ane/4-in) thick air spaces for various effective emissivities and temperature differences.

It tin can exist shown that blanket just ane of the two parallel surfaces facing each other past a material of emissivity east reduces the effective emissivity nearly to ε. Therefore, information technology is usually more economic to glaze only i of the facing surfaces. Note from Fig. 44 that coating one of the interior surfaces of a dou-blepane window with a fabric having an emissivity of 0.1 reduces the rate of heat transfer through the center section of the window past one-half.

Figure 44
The variation of the U-gene for the center section of double- and triple-pane windows with uniform spacing betwixt the panes.

ii. Minimize conduction heat transfer through air space. This tin can exist done by increasing the distance d betwixt the ii glasses. However, this cannot be washed indefinitely since increasing the spacing beyond a critical value initiates convection currents in the enclosed air infinite, which increases the heat transfer coefficient and thus defeats the purpose. Besides, increasing the spacing also increases the thickness of the necessary framing and the price of the window.

Experimental studies have shown that when the spacing d is less than most xiii mm, there is no convection, and estrus transfer through the air is by conduction. Just equally the spacing is increased further, convection currents announced in the air space, and the increase in heat transfer coefficient offsets any benefit obtained by the thicker air layer. Every bit a outcome, the heat transfer coefficient remains near constant, as shown in Fig. 44. Therefore, it makes no sense to utilize an air space thicker than xiii mm in a double-pane window unless a thin polyester film is used to divide the air infinite into two halves to suppress convection currents. The film provides added insulation without adding much to the weight or cost of the double-pane window. The thermal resistance of the window can be increased farther by using triple- or quadruple-pane windows whenever it is economical to do so. Note that using a triple-pane window instead of a double-pane reduces the charge per unit of oestrus transfer through the center section of the window by well-nigh one-third.

Another way of reducing conduction heat transfer through a double-pane window is to use a less-conducting fluid such equally argon or krypton to fill the
gap betwixt the glasses instead of air. The gap in this example needs to be well sealed to prevent the gas from leaking outside. Of form, another culling is to evacuate the gap between the spectacles completely, but it is not practical to do so.

Edge-of-Glass U-Factor of a Window

The glasses in double- and triple-pane windows are kept apart from each other at a compatible distance by spacers fabricated of metals or insulators like aluminum, fiberglass, wood, and butyl. Continuous spacer strips are placed effectually the drinking glass perimeter to provide edge seal likewise as uniform spacing. Nevertheless, the spacers as well serve as undesirable "thermal bridges" between the spectacles, which are at different temperatures, and this short-circuiting may increment heat transfer through the window considerably. Heat transfer in the edge region of a window is two-dimensional, and lab measurements indicate that the edge effects are limited to a six.five-cm-wide band around the perimeter of the drinking glass.

Effigy 45
The edge-of-glass U-factor relative to the middle-of glass U- for windows with diverse spacers.

The U-factor for the edge region of a window is given in Fig. 45 relative to the U-cistron for the center region of the window. The curve would be a
directly diagonal line if the two U-values were equal to each other. Annotation that this is nigh the example for insulating spacers such every bit wood and fiberglass. Just the U-cistron for the edge region can be twice that of the center region for conducting spacers such equally those made of aluminum. Values for steel spacers fall between the two curves for metal and insulating spacers. The edge event is not applicable to single-pane windows.

Frame U-Gene

The framing of a window consists of the entire window except the glazing. Heat transfer through the framing is difficult to determine considering of the different window configurations, different sizes, different constructions, and unlike combination of materials used in the frame structure. The blazon of glazing such equally unmarried pane, double pane, and triple pane affects the thickness of the framing and thus rut transfer through the frame. Near frames are fabricated of wood, aluminum, vinyl, or fiberglass. However, using a combination of these materials (such every bit aluminum-clad wood and vinyl-clad aluminum) is also common to improve advent and durability.

Aluminum is a pop framing material considering it is inexpensive, durable, and piece of cake to manufacture, and does non rot or absorb water similar wood. Still, from a rut transfer betoken of view, it is the to the lowest degree desirable framing cloth because of its loftier thermal conductivity. It will come as no surprise that the U-factor of solid aluminum frames is the highest, and thus a window with aluminum framing volition lose much more than heat than a comparable window with wood or vinyl framing. Estrus transfer through the aluminum framing members can be reduced by using plastic inserts betwixt components to serve equally thermal barriers. The thickness of these inserts profoundly affects rut transfer through the frame. For aluminum frames without the plastic strips, the primary resistance to rut transfer is due to the interior surface rut transfer coefficient. The U-factors for various frames are listed in Table 17 as a function of spacer materials and the glazing unit of measurement thicknesses. Note that the U-factor of metal framing and thus the rate of oestrus transfer through a metallic window frame is more 3 times that of a wood or vinyl window frame.

Interior and Exterior Surface Rut Transfer Coefficients

Heat transfer through a window is besides affected by the convection and radiation rut transfer coefficients betwixt the drinking glass surfaces and surroundings. The furnishings of convection and radiations on the inner and outer surfaces of glazings are usually combined into the combined convection and radiation heat transfer coefficients how-do-you-do and ho, respectively. Under yet air conditions, the combined heat transfer coefficient at the inner surface of a vertical window tin can exist determined from

where T_g = glass temperature in K, T_i = indoor air temperature in K, ε_g = emissivity of the inner surface of the drinking glass exposed to the room (taken to be 0.84 for uncoated glass), and s σ = v.67 x x^-8 W/m² · K⁴ is the Stefan–Boltzmann constant. Here the temperature of the interior surfaces facing the window is assumed to be equal to the indoor air temperature. This
assumption is reasonable when the window faces mostly interior walls, just it becomes questionable when the window is exposed to heated or cooled
surfaces or to other windows. The normally used value of h_i for peak load calculation is

which corresponds to the winter design conditions of T_i = 22ºC and T_thousand = -7ºC for uncoated glass with ε_m = 0.84. But the aforementioned value of hello can likewise exist used for summertime design atmospheric condition as it corresponds to summer conditions of T_i = 24ºC and T_g = 32ºC. The values of h_i for diverse temperatures and glass emissivities are given in Table 18. The commonly used values of ho for peak load calculations are the same every bit those used for outer wall surfaces (34.0 Westward/m² · ºC for winter and 22.7 W/m² · ºC for summer).

Overall U-Factor of Windows

The overall U-factors for various kinds of windows and skylights are evaluated using computer simulations and laboratory testing for winter design conditions; representative values are given in Table nineteen. Exam data may provide more than authentic information for specific products and should exist preferred when available. Notwithstanding, the values listed in the table can be used to obtain satisfactory results under various conditions in the absence of production-specific data. The U-cistron of a fenestration product that differs considerably from the ones in the table can exist determined by (one) determining the fractions of the area that are frame, centre-of-drinking glass, and edge-of-glass (assuming a 65-mm-wide ring around the perimeter of each glazing), (two) determining the U-factors for each department (the centre-of-drinking glass and edge-of-glass U-factors tin can be taken from the first two columns of Table 19 and the frame U-factor can exist taken from Tabular array 18 or other sources), and (three) multiplying the area fractions and the U-factors for each section and adding them upwards (or from Eq. 34 for U_window).

Glazed wall systems can be treated as stock-still windows. Also, the data for double-door windows tin can be used for single-glass doors. Several observations can be made from the data in the table:

1. Skylight U-factors are considerably greater than those of vertical windows. This is because the skylight surface area, including the adjourn, can exist xiii to 240 per centum greater than the rough opening expanse. The gradient of the skylight besides has some outcome.

2. The U-factor of multiple-glazed units can be reduced considerably by filling cavities with argon gas instead of dry air. The performance of CO2-filled units is similar to those filled with argon. The U-factor can be reduced fifty-fifty further by filling the glazing cavities with krypton gas.

three. Coating the glazing surfaces with low-e (depression-emissivity) films reduces the U-factor significantly. For multiple-glazed units, it is acceptable to coat i of the two surfaces facing each other.

4. The thicker the air space in multiple-glazed units, the lower the U-factor, for a thickness of up to 13 mm ( in) of air space. For a specified number of glazings, the window with thicker air layers will have a lower U-gene. For a specified overall thickness of glazing, the higher the number of glazings, the lower the U-factor. Therefore, a triple-pane window with air spaces of 6.four mm (2 such air spaces) will have a lower U-value than a double-pane window with an air space of 12.7 mm.

5. Wood or vinyl frame windows have a considerably lower U-value than comparable metal-frame windows. Therefore, wood or vinyl frame windows are called for in energy-efficient designs.